Problem: Rewrite as a simplified fraction. ${3.82\overline{6} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3826.6666...\\ 100x &= 382.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 3444}$ ${x = \dfrac{3444}{900}} $ ${x = \dfrac{287}{75}} \text{or} {3 \dfrac{62}{75}}$